Question

In Exercises 11–15 find a power series solution to (1+2x^2)y''+(2-3x)y'+4y

Answer #1

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

find dy/dx
a. (x+y)^4 =4y-9x
b. y= (x +6)^2x
c. y= cos^-1 (3x^2 -5x +1 )

Non homogeneous eq w constant; undetermined coefficients
Find the general solution:
1) y" + 4y' + 4y = xe^−x.
2) y" + 2y' + 5y = e^2x cos x.
Determine a suitable form for a particular solution z = z(x) of
the given equations
1) y" + 2y' = 2x + x^2e^−3x + sin 2x.
2) y" − 5y' + 6y = 2e^2x cos x − 3xe^3x + 5.
3) y" + 5y' + 6y = 2e^2x cos x −...

Power series
Find the particular solution of the differential equation:
(x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1.
Use only the 7th degree term of the solution. Solve for y at x=2.
Write your answer in whole number.

Solve the differential equation
(2x+y′+3)y′′=3x+4y′−1

Let y=2−3x+∑n=2∞an x power n be the power series solution of the differential equation:
y″+6xy′+6y=0 about x=0. Find a4.

Find the solution to the initial-value problem: y''+4y=2sin(2x),
y(0)=1, y'(0)=0

(differential equations): solve for x(t) and y(t)
2x' + x - (5y' +4y)=0
3x'-2x-(4y'-y)=0
note: Prime denotes d/dt

Find a series solution for the differential equation 4y'+ y =
0

find a complete solution of each of the following equation
(1) y''-4y'+5y= e^(2x)+24sinx

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